Abstract:Let $F$ be a totally real field and $E$ be a quadratic CM extension field of $F$. Let $n$ be an odd positive integer. Yamana constructed a lift from Hermitian modular forms to automorphic forms on the unitary group. We denote by $\mathrm{I}_n(f)$ the form obtained by applying this lift to the Hermitian modular form $f$ of weight $(\kappa_v)_{v|\infty}$ and level 1. We then express the period $\perd{\mathrm{I}_n(f), \mathrm{I}_n(f)}$ of $\mathrm{I}_n(f)$ for Hecke eigenforms $f$ in terms of special values of certain $L$-functions attached to $f$. This is an extension of Katsurada's result concerning Ikeda's conjecture.
| Comments: | 53 page,v2: corrected the value of Tamagawa numbers and revised main results; definition of Tamagawa measures added, proof on double cosets expanded, and minor stylistic issues fixed |
| Subjects: | Number Theory (math.NT) |
| MSC classes: | 11F67 |
| Cite as: | arXiv:2605.18294 [math.NT] |
| (or arXiv:2605.18294v2 [math.NT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.18294 arXiv-issued DOI via DataCite |
From: Jin Higashitani [view email]
[v1]
Mon, 18 May 2026 12:17:55 UTC (39 KB)
[v2]
Fri, 22 May 2026 07:37:19 UTC (41 KB)
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